Related papers: From Vlasov-Poisson to Schr\"odinger-Poisson: dark…
We report on a new 3D numerical code designed to solve the Einstein equations for general vacuum spacetimes. This code is based on the standard 3+1 approach using cartesian coordinates. We discuss the numerical techniques used in developing…
We consider a perturbative approach to the Vlasov-Poisson system for cosmic structure formation that does not rely on any truncation of the momentum-cumulant hierarchy. The generally non-trivial linear solution is computed by solving a…
A Schr\"odinger-picture description of the evolving quantum state of Hawking radiation is given, based on an ADM decomposition using time slicings that smoothly cross the horizon. This treatment avoids requiring a role for trans-planckian…
The Gell-Mann & Low theorem is a cornerstone of Quantum Field Theory (QFT) and condensed matter physics, and many-body perturbation theory is a foundational tool for treating interactions. However, their integration into quantum algorithms…
In this paper we consider linear, time dependent Schr\"odinger equations of the form $i \partial_t \psi = K_0 \psi + V(t) \psi $, where $K_0$ is a positive self-adjoint operator with discrete spectrum and whose spectral gaps are…
We present the construction of stationary boson-fermion spherically symmetric configurations governed by Newtonian gravity. Bosons are described in the Gross-Pitaevskii regime and fermions are assumed to obey Euler equations for an inviscid…
Stochastic differential equations (SDEs), which models uncertain phenomena as the time evolution of random variables, are exploited in various fields of natural and social sciences such as finance. Since SDEs rarely admit analytical…
We present numerical solutions to Einstein's equations describing large spherical cosmic voids constituted by two components; dark matter and baryons, with a non-vanishing initial relative velocity, in an asymptotically homogeneous…
We consider the relativistic Vlasov--Maxwell (RVM) equations in the limit when the light velocity $c$ goes to infinity. In this regime, the RVM system converges towards the Vlasov--Poisson system and the aim of this paper is to construct…
Fusion plasma and space plasma are typical non-equilibrium and nonlinear systems, with the interactions between different species well described by the Vlasov-Fokker-Planck (VFP) equations. The transport of mass, momentum, energy, and…
The inclusion of spatial smoothing in finite-dimensional particle-based Hamiltonian reductions of the Vlasov equation are considered. In the context of the Vlasov-Poisson equation (and other mean-field Lie-Poisson systems), smoothing…
The variational multiscale (VMS) formulation formally segregates the evolution of the coarse-scales from the fine-scales. VMS modeling requires the approximation of the impact of the fine scales in terms of the coarse scales. In linear…
We investigate the global well-posedness of the ionic Vlasov-Poisson-Boltzmann system which models the evolution of dilute collisional ions. This system distinguishes the electronic Vlasov-Poisson-Boltzmann system via an additional…
The current paradigm for understanding galaxy formation in the universe depends on the existence of self-gravitating collisionless dark matter. Modeling such dark matter systems has been a major focus of astrophysicists, with much of that…
This work develops and explores a quantum-based theory which enables the nature and origin of cold dark matter (CDM) to be understood without need to introduce exotic particles. The quantum approach predicts the existence of certain…
We examine several numerical techniques for the calculation of the dynamics of quantum systems. In particular, we single out an iterative method which is based on expanding the time evolution operator into a finite series of Chebyshev…
Tensor-network simulations of quantum many-body dynamics are fundamentally limited by entanglement build-up, which leads to exponentially growing computational costs. Furthermore, these classical simulation algorithms are inherently…
Many astrophysical simulations involve extreme dynamic range of timescales around 'special points' in the domain (e.g. black holes, stars, planets, disks, galaxies, shocks, mixing interfaces), where processes on small scales couple strongly…
For almost 75 years, the general solution for the Schr\"odinger equation was assumed to be generated by an exponential or a time-ordered exponential known as the Dyson series. We study the unitarity of a solution in the case of a singular…
Describing general quantum many-body dynamics is a challenging task due to the exponential growth of the Hilbert space with system size. The time-dependent variational principle (TDVP) provides a powerful tool to tackle this task by…